public class Solution4 {
    public int[][] matrixBlockSum(int[][] mat, int k) {
        int m = mat.length;
        int n = mat[0].length;
        int[][] dp = new int[m + 1][n + 1];
        //1. 预处理前缀和矩阵
        for(int i = 1; i <= m; i ++) {
            for(int j = 1; j <= n; j++) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1] - dp[i -1][j - 1] + mat[i -1][j - 1];
            }
        }
        //2. 使用
        int[][] ret = new int [m][n];
        for(int i =0; i < m; i++) {
            for(int j = 0; j < n; j++) {
                int x1 = Math.max(0, i - k) + 1;
                int y1 = Math.max(0, j - k) + 1;
                int x2 = Math.min(m - 1, i + k) + 1;
                int y2 = Math.min(n - 1, j + k) + 1;
                ret[i][j] = dp[x2][y2] - dp[x1 - 1][y2] - dp[x2][y1 - 1] + dp[x1 - 1][y1 - 1];
            }
        }
        return ret;
    }
}
